This invention relates to surface acoustic wave sampled data filters which can be utilized as serial access read-only-memories to directly implement at carrier frequencies a coherent fast-frequency-hop synthesizer in the VHF and UHF ranges. The frequency synthesis scheme uses a surface acoustic wave (SAW) discrete chirp filter.
To show, briefly, the evolution of frequency synthesizers, originally, a knob, of an audio oscillator, for example, was turned and the value of an index marker at the knob was read. Later on, programmable frequency synthesizers were developed, which do not require manually turning a knob, wherein servo motors cause rotation of the equivalent of a knob to automatically choose a sequence of frequencies. An electrical signal of the proper code is supplied.
A frequency hopper is an extension of a frequency synthesizer, except the term frequency "hopping" implies that the frequency selection is done rapidly, compared to the speed of frequency selection in the programmable frequency synthesizer. Frequency hopping is often done in the context of spread spectrum communications systems.
Many types of frequency synthesizers have been developed over the years, but only recently have read-only-memory (ROM) synthesizers begun to reach maturity. This has occurred primarily because of the advent of sine-cosine lookup tables implemented in digital hardware. Comprehensive background material regarding non-ROM-based frequency synthesizers is furnished by Kroupa, Venceslav F., Frequency Synthesis, Halsted Press/John Wiley, New York, 1973. ROM-based synthesis is discussed in references hereinbelow.
However, other types of ROM devices are becoming available, and, in particular, surface acoustic wave (SAW) devices are starting to serve this purpose. ROM synthesis is particularly suited for applications which require coherent fast frequency hopping. SAW ROM technology makes possible the direct extension of ROM synthesis into the VHF and UHF ranges.
There are several prior art methods used to synthesize a sampled sinusoid using discrete ROMs. One method utilizes one period of a sampled sinusoid stored in sequential order in a random access ROM. These methods are described in Tierney, Joseph, Charles M. Rader, and Bernard Gold, "A Digital Frequency Synthesizer," IEEE Trans. Audio and Electroacoustics, Vol. AU-19, March 1971, pp. 48-57, and Hosking, Rodger H., "Direct Digital Frequency Synthesis," 1973 IEEE Intercon Technical Papers, Section 34/1, New York, 1973.
If all samples of the ROM are read in sequence with a sample time interval .DELTA.t, then a sinusoid of period T and frequency f.sub.o is generated, where T = N .DELTA.t = 1/f.sub.o. However, if every kth sample is read with the same sample interval .DELTA.t, then the frequency of the generated sinusoid is kf.sub.o. Since k can take on the values 0,1, . . . , N-1, a total of N frequencies which are all harmonically related can be generated. The sampling ambiguity called aliasing may be evident depending upon whether complex or real sinusoids are generated.
A second method for the generation of sampled sinusoids has special application in SAW technology because it utilizes serial-access ROMs. This method consists in multiplying the outputs of two N-sample discrete chirp ROMs whose serial readouts are mutually processed by m samples to synthesize the frequency mf.sub.0. For complex ROMs of the form exp(j.pi.n.sup.2 /N), the product takes the form EQU esp(j.pi.n.sup.2 /N) exp(-j.pi.(n-m).sup.2 /N) = exp(j2.pi.mn/N) exp(-j.pi.m.sup.2 /N), (1)
where n corresponds to the time index and m corresponds to the frequency index. The right hand side of this equation can be interpreted as a sampled complex sinusoid of frequency index m multiplied by a complex phase shift which is dependent only on m. It will also be noted that exp(j.pi.n.sup.2 /N) is a periodic function with period N .DELTA.t (N even) or 2 N .DELTA.t (N odd). This second prior art method has an equivalent continuous time (non-sampled) implementation utilizing a corresponding continuous SAW ROM.
For frequency hopping applications, either of these two methods requires a hopping interval equal to or greater than T = N .DELTA.t so that at least one period of each frequency is synthesized with a common nominal bandwidth less than or equal to 1/T. Thus, the maximum hopping rate for these types of synthesizers is equal to f.sub.o. Synthesis may take place at a carrier frequency f.sub.c, in which case f.sub.o refers to the "fundamental" frequency which would be observed if the comb-like band of harmonics to be generated at the carrier f.sub.c were shifted to baseband.
Synthesis via read-only-memory is attractive because it makes possible the coherent generation of a harmonic group of discrete frequencies. These frequencies all will start with known initial phases, and use of this a priori information can be made to build coherent receivers capable of recognizing particular phase relationships among sequentially-produced tone bursts within the operating band of the synthesizer.
ROM synthesis is also attractive because nearly instantaneous changes can be made when hopping from one frequency to the next. In contrast, a phase-lock-loop synthesizer invariably requires several periods of the waveform being synthesized before a stable lock is acquired.
Discrete chirp transversal filters have been used in the prior art as elements in chirp-Z transform (CZT) processor systems. Such use has been, for example, described by Alsup, J. M., R. W. Means, and H. J. Whitehouse, "Real Time Discrete Fourier Transforms Using Surface Acoustic Wave Devices," Proc. IEE International Specialist Seminar on Component Performance and Systems Application of Surface Acoustic Wave Devices, Aviemore, Scotland, Sept. 24-28, 1973; and by Alsup, J. M., "Surface Acoustic Wave CZT Processors," Proceedings 1974 Ulltrasonics Symposium, Milwaukee, Wis., Nov. 1974, pp. 378-381.
Such filters may be regarded as acoustic ROMs and used to implement coherent frequency synthesis. Periodic impulsing of such a SAW discrete chirp filter will result in periodic generation of the function exp(j.pi.n.sup.2 /N) on a carrier, so that two such ROMs operating at carrier frequencies f.sub.1 and f.sub.2 can provide the necessary signals to generate a tone burst over the duration of the ROM outputs. This tone is obtained by delaying one signal with respect to the other and multiplying the two ROM outputs: EQU p(t-n .DELTA.t) cos[2.pi.f.sub.1 t + .pi.n.sup.2 /N] p(t-n .DELTA.t) cos[2.pi.f.sub.2 t - .pi.(n-m).sup.2 /N] = p.sup.2 (t-n .DELTA.t) cos[2.pi.(f.sub.1 +f.sub.2)t + 2.pi.mn/N - .pi.m.sup.2 /N] + (f.sub.1 -f.sub.2)-term, (2)
where p(t) is the sampling window, e.g., EQU p(t) = 1, 0&lt;t&lt; .DELTA.t, and p(t) = 0 otherwise. (3)
The second SAW chirp ROM output is identical to that of the first one except that it is delayed by an amount m .DELTA.t, and its modulation is the complex conjugate of that of the first ROM, which is equivalent to a negative frequency slope. Since m can vary over the interval 0, 1, . . . , N-1 in an arbitrary order, control over the hopping sequence is flexible.
Discrete chirp ROMs are also useful since they can be used to generate a given sinusoid within the band of operation for an arbitrary length of time. This property is important for applications where frequency hopping is required on a part-time basis only. Continuous SAW chirp filters can also be used as ROMs in a similar sum or difference frequency scheme, but care must be taken to account for possible discontinuities where end-points of the chirp function are encountered. Such use is described by Atzeni, C., G. Manes, and L. Masotti, "Signal Processing by Analog Chirp-Transformation Using SAW Devices," IEEE 1975 Ultrasonics Symposium Proceedings, Los Angeles, CA, Sept. 1975, Paper G-6.